Exponent Problems

Product of Powers

Simplify:

Product of Powers

What is the rule for product of powers?


Make your own problem and solve it.

Pre-Skill Review

Complete #4, 5, and 8.

Word Problem

Farmer Peter and Farmer Paula are picking apples from their apple trees. Farmer Peter as already picked 287 apples. Farmer Peter picks another 5 apples each minute. Farmer Paula has already picked 154 apples. Farmer Paula picks another 6 apples each minute.

How long will it take for Peter and Paula to pick the same number of apples?



After 10 minutes who has picked more apples, Peter or Paula?

Application Problems

You want to go to your uncle’s house. You have two options. Option A is to take a taxi which will cost you $10 plus $1.5 per additional mile. Option B is to drive by yourself. The cost of gasoline is $2 per mile. 

Write a system of equations in order to solve this problem.


After how many miles will the total costs of the two options be the same? 

Word Problems

Jared can make one Christmas ornament a minute, and he already has five made. Marissa can make three ornaments every two minutes, but does not have any made.


 If they both start working at the same time, how many minutes will it take for Marissa and Jared to have the same number of ornaments made?



How many ornaments does each have made when they are tied?

Writing Equations

Wendy is starting a catering business and is attempting to figure out who she should be using to transport the food to different locations. She has found two trucking companies that are willing to make sure her food arrives intact. Peter’s Pick Up charges $0.40 per mile and charges a flat fee of $68. Helen’s Haulers charges $0.65 per mile and charges a flat fee of $23.

Application Problems

The state fair is a popular field trip destination. This year the senior class at High School A and the senior class at High School B both planned trips there. The senior class at High School A rented and filled 8 vans and 8 buses with 240 students. High School B rented and filled 4 vans and 1 bus with 54 students. Every van had the same number of students in it as did the buses. Find the number of students in each van and in each bus.

System Word Problems

Castel and Gabriella are selling pies for a school fundraiser. Customers can buy apple pies and lemon meringue pies. Castel sold 6 apple pies and 4 lemon meringue pies for a total of $80. Gabriella sold 6 apple pies and 5 lemon meringue pies for a total of $94. What is the cost each of one apple pie and one lemon meringue pie?

Word Problems

Kristin spent $131 on shirts. Fancy shirts cost $28 and plain shirts cost $15. If she bought a total of 7 then how many of each kind did she buy?

Basic Word Problems

The sum of two numbers is 17.  The difference is 3.  Find the two numbers.

Elimination Method

3 + 2x − y = 0
−3 − 7y = 10x

Opposites

Make each pair of numbers opposites:

-7     and      14

-8     and      10

Elimination Method

Complete the following problem using the Elimination Method:

3x - 2y = 2
5x - 5y = 10

Elimination Method

Use the Elimination Method to solve:

5x + y = 9
10x − 7y = −18

Elimination Method

Use the Elimination Method:

2x + y = 7
3x - y = 3

Opposites

Identify the opposites of...

#1.  -3

#2.  0

#3.  -17

#4.  4

#5.  12

Substitution

y = -3x + 10
y = 5x - 12

Substitution Method

Use the substitution method:

y = 9x + 8

y = x – 8

Substitution Method

Complete this problem using the Substitution Method

y = 3x + 1
4y = 12x + 4

Using Substitution

Solve by doing substitution

 y = 6x − 11
−2x − 3y = −7

Substitution Method

Solve by using the substitution method:

y = -3x - 13
-x - 2y = -4

Substitution

Complete the substitution problem:

      y = 3
      2x + 3y = 15

Substitution Method

Solve this system of equations using the substitution method:

2x + 3y = 4
y = 5x - 27

Progress Check Reflection

Look through your progress check and see where you went wrong.  What mistakes did you make?  Which problems did you get wrong that you thought you did correctly?  What help do you need from us to get yourself to a level 3 or better?

Graphing Equations Using a Computer Program

Go to the link below:

https://www.ixl.com/math/algebra-1/solve-a-system-of-equations-by-graphing

Complete the first problem and reply with the answer you submitted.

Graphing Method

Solve:

-2x - y - 1 = 0
-6x - 3y - 3 = 0

Graphing Method

Graph the following equations and reply with the solution:

y = 3x - 4
y = -1/2x + 3

Systems of Equations

Determine the solution:

3x - 6y = 18

2x + 2y = 2

Graphing Method

Solve each system by graphing.

y = -5/3x + 3

y = 1/3x - 3

Graphing Equations

Graph the following equation:

2x + 4y = -16

When you are done graphing your equation have either Ms. O or Mrs. Fournier check your work!

Reply to this post with your rearranged equation. 

Solution

What are the three different types of solutions for a system of equations?